Solve 4cos(2x)=2 for the smallest three positive solutions.

Question

answers accurate to at least two decimal places, as a list separated by commas

Answer 1

4cos(2x) = 2

Divide both sides by 4, and get

cos(2x) = 1/2

The cosine of π/3 is the smallest positive solution of the argument of a cosine such that the cosine equals 1/2. So, 2x = π/3, or x = π/6.

The lowest three positive solutions to cos(θ) = 1/2 are π/3, π/3 + 2π = 7/3 π, and π/3 + 4π = 13/3 π. Therefore, the lowest three solutions for x are:

π/6, 7/6 π, 13/6 π radians

or

60, 420, 780 degrees